LMI-based robust tracking of a class of MIMO nonlinear systems

Mukherjee, Arunima; Sengupta, Anindita

doi:10.1007/s12046-019-1182-1

Cited by 3 publications

(3 citation statements)

References 30 publications

(42 reference statements)

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“…Two MIMO nonlinear systems are implemented based on CEPD control method by MATLAB software. Moreover, the traditional SMC method, robust adaptive fuzzy (RAF) control approach, recurrent type‐2 fuzzy radial basis neural network‐based sliding mode control (RT2FRBFNSMC), and LMI‐based robust tracking control (LMIRTC) reported by previous studies [35–37] are employed to validate the superiority of the proposed method. To compromise between the new method with other approaches, the indexes integral square error (ISE) and integral absolute error (IAE) are calculated and presented.…”

Section: Numerical Simulationsmentioning

confidence: 99%

Lumped uncertainty alleviation in output channels of MIMO nonlinear systems based on robust disturbance observer‐based control strategy

Zarei

Tavakoli

2022

Asian Journal of Control

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Disturbances and uncertainties can produce unsatisfactory responses in many industrial and engineering systems. Besides, the practical systems and processes are multiple‐input multiple‐output (MIMO). Hence, achieving a good control performance with adequate output responses is not simple. Many different methods were provided for control of industrial processes in some references. However, in this paper, the primary goal is to design an appropriate tracking controller for alleviating the destructive effects of uncertainties in output channels of MIMO nonlinear systems. For this purpose, a robust mechanism has been introduced according to the optimal design of centralized extended proportional‐derivative (CEPD) and disturbance observer (DOB). By designing the derivative part Kd$$ {K}_d $$ based on famous Vandermonde matrix and DOB gain normalΓ$$ \Gamma $$, the robust criterion R=()I+CGKd−1$$ R&amp;#x0003D;{\left(I&amp;#x0002B; CG{K}_d\right)}&amp;#x0005E;{-1} $$ is obtained to tackle the undesirable factors such as nonlinear functions and uncertainties in error dynamics. The closed‐loop stability is guaranteed by tuning the proportional part Kp$$ {K}_p $$ under linear matrix inequality. The proposed scheme in this paper can be used for a wide range of MIMO nonlinear systems in practical situations.

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Section: Numerical Simulationsmentioning

confidence: 99%

Lumped uncertainty alleviation in output channels of MIMO nonlinear systems based on robust disturbance observer‐based control strategy

Zarei

Tavakoli

2022

Asian Journal of Control

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“…Because the suggested design condition is bilinear in the choice variables, an iterative approach is also suggested. In [48], the input to state-stability Lyapunov functions was used to develop an LMI-framed linear-state variable feedback control scheme for MIMO Lipschitz nonlinear systems with bounded parameter uncertainty. The authors of [49,50] addressed the problem of observer-based robust control for nonlinear uncertain systems.…”

Section: Introductionmentioning

confidence: 99%

“…For example, the work proposed in [30][31][32][33][34] satisfies the requirement of uncertain linear systems, whereas [35] considers nominal linear systems in the presence of disturbances. Uncertain nonlinear systems were investigated in [47][48][49][50]. Additionally, most of the above approaches make some assumptions and impose limitations on the system, such as Lipschitzian nonlinearities.…”

Section: Introductionmentioning

confidence: 99%

H∞ Robust LMI-Based Nonlinear State Feedback Controller of Uncertain Nonlinear Systems with External Disturbances

Chatavi

Mobayen

et al. 2022

Mathematics

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In this paper, we propose a nonlinear state feedback controller based on linear matrix inequality (LMI) for a class of nonlinear systems with parametric uncertainties and external disturbances. The primary goals of the proposed controller are to guarantee system stability and performance in the presence of system uncertainties and time-dependent disturbances. To meet the specified objectives, the LMI form is calculated as a hierarchical control structure. Using the Lyapunov stability function, the asymptotic stability of the nominal system obtained from the nonlinear state feedback is proven, and the LMI condition is attained. After applying the nonlinear state feedback controller, asymptotic stability conditions for the nominal system are constructed using the Lyapunov function, and the nonlinear state-feedback control mechanism is determined accordingly. Considering the external disturbance as input, the terms of the state matrices are substituted in the obtained LMI, and the LMI condition for a nominal system is achieved in the presence of disturbances. The asymptotic stability condition of the uncertain system in the presence of external disturbances is determined by adding uncertainties to the system. The proposed approach yields a simple control mechanism representing an independent of system order. The performance of the proposed approach was assessed using a simulation study of a ball and beam system.

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Reference tracking and transient response shaping of uncertain quasi one-sided Lipschitz nonlinear systems

Mukherjee

Sengupta

2021

Journal of Control and Decision

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LMI-based robust tracking of a class of MIMO nonlinear systems

Cited by 3 publications

References 30 publications

Lumped uncertainty alleviation in output channels of MIMO nonlinear systems based on robust disturbance observer‐based control strategy

Lumped uncertainty alleviation in output channels of MIMO nonlinear systems based on robust disturbance observer‐based control strategy

H∞ Robust LMI-Based Nonlinear State Feedback Controller of Uncertain Nonlinear Systems with External Disturbances

Reference tracking and transient response shaping of uncertain quasi one-sided Lipschitz nonlinear systems

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